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<meta name="citation_title" content="Global discharging methods for coloring problems in graphs" />
<meta name="DC.title" content="Global discharging methods for coloring problems in graphs" />
<meta property="og:title" content="Global discharging methods for coloring problems in graphs" />
<meta name="DC.identifier" content="https://theses.hal.science/tel-02083632" />
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    <meta name="citation_author" content="Marthe Bonamy" />

            
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                <meta name="citation_author_institution" content="Algorithmes, Graphes et Combinatoire" />
        <meta name="DC.creator" content="Marthe Bonamy" />


    <meta name="citation_abstract" content="This thesis falls within graph theory, and deals more precisely with graph coloring problems. In this thesis, we use and develop the discharging method, a counting argument that makes strong advantage of the graph structure. This method is decisive in the proof of the Four Color Theorem. We first give an illustrated overview of the discharging tools that are used for this work: nice methods that we apply, and handy tricks that we develop. In particular, we present the main ideas in a global discharging argument. In the realm of list edge coloring, we most notably prove that the weak List Coloring Conjecture is true for planar graphs of maximum degree 8 (i.e. that they are edge 9-choosable), thus improving over a result of Borodin from 1990. We finally present our results about square coloring, where the goal is to color the vertices in such a way that two vertices that are adjacent or have a common neighbor receive different colors. We look in particular into sufficient conditions on the density of a graph (i.e. the maximum average degree of a subgraph) for its square to be colorable with few colors." />
    <meta name="DC.description" content="This thesis falls within graph theory, and deals more precisely with graph coloring problems. In this thesis, we use and develop the discharging method, a counting argument that makes strong advantage of the graph structure. This method is decisive in the proof of the Four Color Theorem. We first give an illustrated overview of the discharging tools that are used for this work: nice methods that we apply, and handy tricks that we develop. In particular, we present the main ideas in a global discharging argument. In the realm of list edge coloring, we most notably prove that the weak List Coloring Conjecture is true for planar graphs of maximum degree 8 (i.e. that they are edge 9-choosable), thus improving over a result of Borodin from 1990. We finally present our results about square coloring, where the goal is to color the vertices in such a way that two vertices that are adjacent or have a common neighbor receive different colors. We look in particular into sufficient conditions on the density of a graph (i.e. the maximum average degree of a subgraph) for its square to be colorable with few colors." />
    <meta name="description" content="This thesis falls within graph theory, and deals more precisely with graph coloring problems. In this thesis, we use and develop the discharging method, a counting argument that makes strong advantage of the graph structure. This method is decisive in the proof of the Four Color Theorem. We first give an illustrated overview of the discharging tools that are used for this work: nice methods that we apply, and handy tricks that we develop. In particular, we present the main ideas in a global discharging argument. In the realm of list edge coloring, we most notably prove that the weak List Coloring Conjecture is true for planar graphs of maximum degree 8 (i.e. that they are edge 9-choosable), thus improving over a result of Borodin from 1990. We finally present our results about square coloring, where the goal is to color the vertices in such a way that two vertices that are adjacent or have a common neighbor receive different colors. We look in particular into sufficient conditions on the density of a graph (i.e. the maximum average degree of a subgraph) for its square to be colorable with few colors." />
    <meta property="og:description" content="This thesis falls within graph theory, and deals more precisely with graph coloring problems. In this thesis, we use and develop the discharging method, a counting argument that makes strong advantage of the graph structure. This method is decisive in the proof of the Four Color Theorem. We first give an illustrated overview of the discharging tools that are used for this work: nice methods that we apply, and handy tricks that we develop. In particular, we present the main ideas in a global discharging argument. In the realm of list edge coloring, we most notably prove that the weak List Coloring Conjecture is true for planar graphs of maximum degree 8 (i.e. that they are edge 9-choosable), thus improving over a result of Borodin from 1990. We finally present our results about square coloring, where the goal is to color the vertices in such a way that two vertices that are adjacent or have a common neighbor receive different colors. We look in particular into sufficient conditions on the density of a graph (i.e. the maximum average degree of a subgraph) for its square to be colorable with few colors." />

            <meta name="citation_keywords" content="coloring;graph theory" />
    <meta name="DC.subject" content="coloring;graph theory" />
    <meta name="keywords" content="coloring;graph theory" />
            <meta name="citation_keywords" content="théorie des graphes;coloration" />
    <meta name="DC.subject" content="théorie des graphes;coloration" />
    <meta name="keywords" content="théorie des graphes;coloration" />

        <meta name="citation_pdf_url" content="https://theses.hal.science/tel-02083632/document" />
    <meta name="DC.identifier" content="https://theses.hal.science/tel-02083632/document" />
    <meta property="og:url" content="https://theses.hal.science/tel-02083632/document" />

<meta name="citation_online_date" content="2019/03/29" />

    <meta name="citation_publication_date" content="2015/02/09" />
<meta name="DC.date" content="2015/02/09" />
<meta name="DC.issued" content="2015/02/09" />

                                                                    <meta name="citation_dissertation_institution" content="Université de Montpellier" />
            <meta name="DC.publisher" content="Université de Montpellier" />
                                                                                                                                                                            
 
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    <title> Global discharging methods for coloring problems in graphs  - TEL - Thèses en ligne</title>
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<div class="col-md-9"><div class="input-group" style="margin-bottom : 10px;"><button class='btn btn-sm btn-default dropdown-toggle form-btn-lang' style=' z-index:0!important;' data-toggle='dropdown' type='button' value='auth_t'>Auteur (multicritères)&nbsp;</button><ul class='dropdown-menu' role='menu' style='max-height: 140px; overflow:auto;'><li class='dropdown-item'><a data-val='auth_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Auteur (multicritères)</a></li><li class='dropdown-item'><a data-val='authFullName_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Auteur : Nom complet</a></li><li class='dropdown-item'><a data-val='authLastName_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Auteur : Nom de famille</a></li><li class='dropdown-item'><a data-val='authFirstName_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Auteur : Prénom</a></li><li class='dropdown-item'><a data-val='authMiddleName_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Auteur : Complément de nom, deuxième prénom</a></li><li class='dropdown-item'><a data-val='authOrganism_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Auteur : Organisme payeur</a></li><li class='dropdown-item'><a data-val='authIdHal_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Auteur : IdHal (chaîne de caractères)</a></li><li class='dropdown-item'><a data-val='authQuality_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Auteur : Fonction</a></li><li class='dropdown-item'><a data-val='authIdHal_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Auteur : personID (entier)</a></li><li class='dropdown-item'><a data-val='authOrganismId_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Auteur : Identifiant de l'organisme payeur</a></li><li class='dropdown-item'><a data-val='authStructId_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Auteur : Identifiant de la structure</a></li><li class='dropdown-item'><a data-val='director_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Directeur de thèse</a></li><li class='dropdown-item'><a data-val='publisher_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Éditeur</a></li><li class='dropdown-item'><a data-val='scientificEditor_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Éditeur scientifique</a></li><li class='dropdown-item'><a data-val='seriesEditor_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Éditeur de la série</a></li></ul>
<input type="text" name="qa[auth_t][]" id="author" value="" class="input-flex form-control input-sm" lang="auth_t" aria-describedby="author-error" style=" " data-keyword="1" /><span class="input-group-btn"><button type='button' class='btn btn-sm btn-primary form-btn-multi form-btn-add' onclick='MultiTextSimpleLangKeywordAdd(this, "qa");' data-toggle='tooltip' data-placement='right' data-original-title='Ajouter'><i class='icon icon-plus'></i> <span> Ajouter</span></button></span></div></div></div>
<div class="form-group row " id="structure-element"><label for="structure" class="col-md-3 control-label optional">Structure</label>
<div class="col-md-9"><div class="input-group" style="margin-bottom : 10px;"><button class='btn btn-sm btn-default dropdown-toggle form-btn-lang' style=' z-index:0!important;' data-toggle='dropdown' type='button' value='structure_t'>Structure (multicritères)&nbsp;</button><ul class='dropdown-menu' role='menu' style='max-height: 140px; overflow:auto;'><li class='dropdown-item'><a data-val='structure_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Structure (multicritères)</a></li><li class='dropdown-item'><a data-val='structAcronym_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Structure : Acronyme</a></li><li class='dropdown-item'><a data-val='structName_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Structure : Nom</a></li><li class='dropdown-item'><a data-val='structCode_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Structure : Code</a></li><li class='dropdown-item'><a data-val='structCountry_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Structure : Pays</a></li><li class='dropdown-item'><a data-val='structType_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Structure : Type</a></li><li class='dropdown-item'><a data-val='structValid_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Structure : État dans le référentiel</a></li><li class='dropdown-item'><a data-val='structId_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Structure : Identifiant HAL de la structure</a></li><li class='dropdown-item'><a data-val='rteamStructCountry_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Structure/équipe de recherche : Pays</a></li><li class='dropdown-item'><a data-val='deptStructCountry_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Structure/regroupement d'équipes : Pays</a></li><li class='dropdown-item'><a data-val='labStructCountry_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Structure/laboratoire : Pays</a></li><li class='dropdown-item'><a data-val='rgrpLabStructCountry_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Structure/regroupement de laboratoires : Pays</a></li><li class='dropdown-item'><a data-val='instStructCountry_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Structure/institution : Pays</a></li><li class='dropdown-item'><a data-val='rgrpInstStructCountry_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Structure/regroupement d'institutions : Pays</a></li></ul>
<input type="text" name="qa[structure_t][]" id="structure" value="" class="input-flex form-control input-sm" lang="structure_t" aria-describedby="structure-error" style=" " data-keyword="1" /><span class="input-group-btn"><button type='button' class='btn btn-sm btn-primary form-btn-multi form-btn-add' onclick='MultiTextSimpleLangKeywordAdd(this, "qa");' data-toggle='tooltip' data-placement='right' data-original-title='Ajouter'><i class='icon icon-plus'></i> <span> Ajouter</span></button></span></div></div></div>
<div class="form-group row " id="qa-element"><label for="qa" class="col-md-3 control-label optional">Autres</label>
<div class="col-md-9"><div class="input-group" style="margin-bottom : 10px;"><button class='btn btn-sm btn-default dropdown-toggle form-btn-lang' style=' z-index:0!important;' data-toggle='dropdown' type='button' value='text'>Champ de recherche par défaut (multicritères)&nbsp;</button><ul class='dropdown-menu' role='menu' style='max-height: 140px; overflow:auto;'><li class='dropdown-item'><a data-val='text' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Champ de recherche par défaut (multicritères)</a></li><li class='dropdown-item'><a data-val='--sep1' href='javascript:void(0);' onclick="LangInit(this, 'qa');"></a></li><li class='dropdown-item'><a data-val='journal_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Revues (multicritères)</a></li><li class='dropdown-item'><a data-val='journalPublisher_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Revue : Éditeur</a></li><li class='dropdown-item'><a data-val='journalTitleAbbr_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Revue : Titre abrégé</a></li><li class='dropdown-item'><a data-val='journalTitle_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Revue : Titre</a></li><li class='dropdown-item'><a data-val='journalId_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Revue : Identifiant interne</a></li><li class='dropdown-item'><a data-val='journalDate_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Revue : Date de début de publication</a></li><li class='dropdown-item'><a data-val='journalEissn_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Revue : ISSN électronique</a></li><li class='dropdown-item'><a data-val='journalIssn_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Revue : ISSN</a></li><li class='dropdown-item'><a data-val='journalPublisher_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Revue : Éditeur</a></li><li class='dropdown-item'><a data-val='journalSherpaColor_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Revue : Couleur dans SHERPA/RoMEO</a></li><li class='dropdown-item'><a data-val='journalValid_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Revue : État dans le référentiel</a></li><li class='dropdown-item'><a data-val='--sep2' href='javascript:void(0);' onclick="LangInit(this, 'qa');"></a></li><li class='dropdown-item'><a data-val='conference_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Colloque (multicritères)</a></li><li class='dropdown-item'><a data-val='conferenceTitle_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Colloque : Titre</a></li><li class='dropdown-item'><a data-val='conferenceOrganizer_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Colloque : Organisateur</a></li><li class='dropdown-item'><a data-val='conferenceStartDateY_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Colloque : date de début (Année)</a></li><li class='dropdown-item'><a data-val='conferenceEndDateY_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Colloque : date de fin (Année)</a></li><li class='dropdown-item'><a data-val='invitedCommunication_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Conférence invitée (oui/non)</a></li><li class='dropdown-item'><a data-val='--sep3' href='javascript:void(0);' onclick="LangInit(this, 'qa');"></a></li><li class='dropdown-item'><a data-val='anrProject_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projets ANR (multicritères)</a></li><li class='dropdown-item'><a data-val='anrProjectAcronym_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet ANR : Acronyme</a></li><li class='dropdown-item'><a data-val='anrProjectAcronymProgram_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet ANR : Acronyme du programme</a></li><li class='dropdown-item'><a data-val='anrProjectReference_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet ANR : Code décision (référence)</a></li><li class='dropdown-item'><a data-val='anrProjectTitle_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet ANR : Nom</a></li><li class='dropdown-item'><a data-val='anrProjectId_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet ANR : Identifiant interne</a></li><li class='dropdown-item'><a data-val='anrProjectValid_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet ANR : État dans le référentiel</a></li><li class='dropdown-item'><a data-val='anses_funding_acronym_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet ANSES: Acronyme</a></li><li class='dropdown-item'><a data-val='anses_funding_reference_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet ANSES: Code decision (reference)</a></li><li class='dropdown-item'><a data-val='anses_funding_title_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet ANSES: Nom</a></li><li class='dropdown-item'><a data-val='ademe_funding_acronym_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet ADEME: Acronyme</a></li><li class='dropdown-item'><a data-val='ademe_funding_reference_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet ADEME: Code decision (reference)</a></li><li class='dropdown-item'><a data-val='ademe_funding_title_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet ADEME: Nom</a></li><li class='dropdown-item'><a data-val='--sep4' href='javascript:void(0);' onclick="LangInit(this, 'qa');"></a></li><li class='dropdown-item'><a data-val='europeanProject_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projets européens (multicritères)</a></li><li class='dropdown-item'><a data-val='europeanProjectAcronym_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet européen : Acronyme</a></li><li class='dropdown-item'><a data-val='europeanProjectCallId_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet européen : Identifiant de l'appel à projet</a></li><li class='dropdown-item'><a data-val='europeanProjectReference_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet européen : Référence</a></li><li class='dropdown-item'><a data-val='europeanProjectTitle_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet européen : Nom</a></li><li class='dropdown-item'><a data-val='europeanProjectEndDate_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet européen : Date de fin</a></li><li class='dropdown-item'><a data-val='europeanProjectFinancing_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet européen : Financement</a></li><li class='dropdown-item'><a data-val='europeanProjectStartDate_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet européen : Date de début</a></li><li class='dropdown-item'><a data-val='europeanProjectValid_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet européen : État dans le référentiel</a></li><li class='dropdown-item'><a data-val='europeanProjectId_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Projet européen : Identifiant interne</a></li><li class='dropdown-item'><a data-val='--sep6' href='javascript:void(0);' onclick="LangInit(this, 'qa');"></a></li><li class='dropdown-item'><a data-val='producedDateY_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Date de production : année</a></li><li class='dropdown-item'><a data-val='releasedDateY_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Date de mise en ligne : année</a></li><li class='dropdown-item'><a data-val='publicationDateY_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Date de publication : année</a></li><li class='dropdown-item'><a data-val='writingDateY_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Date d'écriture : année</a></li><li class='dropdown-item'><a data-val='modifiedDateY_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Date de modification du dépôt : année</a></li><li class='dropdown-item'><a data-val='submittedDateY_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Date de dépôt : année</a></li><li class='dropdown-item'><a data-val='ePublicationDateY_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Date de publication électronique : année</a></li><li class='dropdown-item'><a data-val='--sep7' href='javascript:void(0);' onclick="LangInit(this, 'qa');"></a></li><li class='dropdown-item'><a data-val='collection_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Collection HAL (multicritères)</a></li><li class='dropdown-item'><a data-val='collCategory_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Collection HAL : catégorie</a></li><li class='dropdown-item'><a data-val='collCode_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Collection HAL : Code</a></li><li class='dropdown-item'><a data-val='collName_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Collection HAL : Nom</a></li><li class='dropdown-item'><a data-val='collId_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Collection HAL : Identifiant interne</a></li><li class='dropdown-item'><a data-val='--sep8' href='javascript:void(0);' onclick="LangInit(this, 'qa');"></a></li><li class='dropdown-item'><a data-val='contributorId_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Identifiant interne du contributeur/déposant</a></li><li class='dropdown-item'><a data-val='contributorFullName_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Nom complet du contributeur/déposant</a></li><li class='dropdown-item'><a data-val='--sep9' href='javascript:void(0);' onclick="LangInit(this, 'qa');"></a></li><li class='dropdown-item'><a data-val='domain_t' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Domaines</a></li><li class='dropdown-item'><a data-val='primaryDomain_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Domaine primaire</a></li><li class='dropdown-item'><a data-val='level0_domain_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Domaine racine</a></li><li class='dropdown-item'><a data-val='level1_domain_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Sous-domaine niveau 1</a></li><li class='dropdown-item'><a data-val='level2_domain_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Sous-domaine niveau 2</a></li><li class='dropdown-item'><a data-val='level3_domain_s' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Sous-domaine niveau 3</a></li><li class='dropdown-item'><a data-val='--sep10' href='javascript:void(0);' onclick="LangInit(this, 'qa');"></a></li><li class='dropdown-item'><a data-val='status_i' href='javascript:void(0);' onclick="LangInit(this, 'qa');">Statut du 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                    This thesis falls within graph theory, and deals more precisely with graph coloring problems. In this thesis, we use and develop the discharging method, a counting argument that makes strong advantage of the graph structure. This method is decisive in the proof of the Four Color Theorem. We first give an illustrated overview of the discharging tools that are used for this work: nice methods that we apply, and handy tricks that we develop. In particular, we present the main ideas in a global discharging argument. In the realm of list edge coloring, we most notably prove that the weak List Coloring Conjecture is true for planar graphs of maximum degree 8 (i.e. that they are edge 9-choosable), thus improving over a result of Borodin from 1990. We finally present our results about square coloring, where the goal is to color the vertices in such a way that two vertices that are adjacent or have a common neighbor receive different colors. We look in particular into sufficient conditions on the density of a graph (i.e. the maximum average degree of a subgraph) for its square to be colorable with few colors.
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                    Cette thèse s’inscrit dans le cadre de la théorie des graphes, et porte plus particulièrement sur des problèmes de coloration de graphes. Dans cette thèse, nous nous intéressons à l’utilisation et au développement de la méthode de  déchargement, un argument de comptage qui exploite fortement la structure du graphe. Cette méthode est décisive dans la preuve du Théorème des Quatre Couleurs. Nous donnons d’abord une vue d’ensemble des outils de déchargement que nous utilisons dans ce travail, entre les méthodes élégantes mises en application, et les astuces développées. Nous présentons en particulier l’idée essentielle d’une preuve par déchargement global. Dans le cadre de la coloration d’arêtes par liste, nous résolvons la Conjecture de Coloration par Liste faible dans le cas des graphes planaires de degré maximum 8, en prouvant qu’on peut colorier par liste les arêtes de ces derniers avec 9 couleurs
seulement. Ceci améliore un résultat de Borodin de 1990. Enfin, nous présentons nos résultats dans le cadre de la coloration de carrés, où il s’agit de colorier les sommets sans qu’il y ait deux sommets adjacents ou avec un voisin commun qui soient de la même couleur. On s’intéresse en particulier à des conditions suffisantes sur la densité du graphe (c-à-d le degré moyen maximum d’un sous-graphe) pour qu’on puisse colorier son carré avec peu de couleurs.
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                    <a rel="nofollow" href="/search/index/q/*/contributorId_i/180184" target="_blank">Marthe Bonamy</a>
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    <p>https://theses.hal.science/tel-02083632</p>
    <p>Soumis le : vendredi 29 mars 2019-10:34:19</p>
    <p>Dernière modification le : lundi 8 avril 2024-13:23:18</p>
            <p>Archivage à long terme le : dimanche 30 juin 2019-13:28:05</p>
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                 Marthe Bonamy. Global discharging methods for coloring problems in graphs. Discrete Mathematics [cs.DM]. Université de Montpellier, 2015. English. <a target="_blank" href="https://www.theses.fr/">&#x27E8;NNT : &#x27E9;</a>. <a target="_blank" href="https://theses.hal.science/tel-02083632v1">&#x27E8;tel-02083632&#x27E9;</a>
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